# Homework 03

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## CBE 179 - Homework #03

**Due Friday, 2014.09.26**

As always, state all of the assumptions made in each model and cite your sources.

- Calculate and plot the Maxwell-Boltzmann speed and kinetic energy distributions in N₂ at 300K and 400K. Show mean values on the plots. What fraction of the molecules have a velocity of more than 1500 m/s at each temperature?

*the problem originally misstated the velocity of interest as 1500 cm/s; if you correctly calculated the fraction based on this misprint (which should have been essentially 100%) and already handed it in, that's fine; if not, run the integral again with the updated number*

- Plot mean free path at 300K for air from 1 torr to 760 torr. Use Lennard-Jones estimates for hard sphere radii and collision cross sections.

- Estimate mass diffusivity, viscosity, and thermal conductivity for Ar at 300K and 1 atm using mean free path theory. Compare these values with experimentally-determined values.

- Consider a cylindrical chamber, 100 cm in diameter and 10 cm high. The chamber initially has a monolayer of liquid water (assume 10^15 molecules per square centimeter) on the interior walls. If all this water is released as vapor at 300K, how much does the pressure rise in the chamber?

- Assuming the vacuum chamber in problem #04 has a 1mm diameter hole connecting it to an adjacent chamber maintained at 10^-10 torr, how long would it take to reduce the pressure from the water vapor in the first chamber from 1 torr to 10^-3 torr?

- If the chamber in problem #04 has, instead of a small hole, a very cold (e.g. liquid nitrogen-cooled) surface, this can also act as a kind of pump since the water vapor will condense on every surface collision. How long would it take to reduce the pressure from the water vapor from 1 torr to 10^-3 torr if the cold plate is 100cm in diameter?

- Why is hydrogen a difficult gas to pump with a turbomolecular pump?

- While modern processing techniques enrich fissile uranium from naturally-occurring isotopic mixtures using a gas centrifuge, the Manhattan Project (1942-1946) accomplished this separation with gas diffusion‒based techniques. From the physics of gaseous uranium, how is this separation achieved? What is the best-case enrichment achievable with a gas diffusion cascade system of n stages?